Effects of information and group structure on evolution of altruism: analysis of two-score model by covariance and contextual analyses

An altruistic individual has to gamble on cooperation to a stranger because it does not know whether the stranger is trustworthy before direct interaction. Nowak and Sigmund (Nature 393 (1998a) 573; J. Theor. Biol. 194 (1998b) 561) presented a new theoretical framework of indirect reciprocal altruism by image scoring game where all individuals are informed about a partnerʹs behavior from its image score without direct interaction. Interestingly, in a simplified version of the image scoring game, the evolutionarily stability condition for altruism became a similar form of Hamiltonʹs rule, i.e. inequality that the probability of getting correct information is more than the ratio of cost to benefit. Since the Hamiltonʹs rule was derived by evolutionarily stable analysis, the evolutionary meaning of the probability of getting correct information has not been clearly examined in terms of kin and group selection. In this study, we applied covariance analysis to the two-score model for deriving the Hamiltonʹs rule. We confirmed that the probability of getting correct information was proportional to the bias of altruistic interactions caused by using information about a partnerʹs image score. The Hamiltonʹs rule was dependent on the number of game bouts even though the information reduced the risk of cooperation to selfish one at the first encounter. In addition, we incorporated group structure to the two-score model to examine whether the probability of getting correct information affect selection for altruism by group selection. We calculated a Hamiltonʹs rule of group selection by contextual analysis. Group selection is very effective when either the probability of getting correct information or that of future interaction, or both are low. The two Hamiltonʹs rules derived by covariance and contextual analyses demonstrated the effects of information and group structure on the evolution of altruism. We inferred that information about a partnerʹs behavior and group structure can produce flexible pathways for the evolution of altruism.